Carl Hierholzer
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Carl Hierholzer
Carl Hierholzer (2 October 1840 – 13 September 1871) was a German mathematician. Biography Hierholzer studied mathematics in Karlsruhe, and he got his Ph.D. from Ruprecht-Karls-Universität Heidelberg in 1865. His Ph.D. advisor was Ludwig Otto Hesse (1811–1874). In 1870 Hierholzer wrote his habilitation about conic sections (title: ''Ueber Kegelschnitte im Raum'') in Karlsruhe, where he later became a Privatdozent. Hierholzer proved that a connected graph has an Eulerian trail if and only if exactly zero or two of its vertices have an odd degree. This result had been given, with no proof of the 'if' part, by Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ... in 1736. Hierholzer apparently presented his work to a circle of fellow mathematicians not long before h ...
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Germans
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ...
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Universität Karlsruhe (TH)
The Karlsruhe Institute of Technology (KIT; german: Karlsruher Institut für Technologie) is a public research university in Karlsruhe, Germany. The institute is a national research center of the Helmholtz Association. KIT was created in 2009 when the University of Karlsruhe (), founded in 1825 as a public research university and also known as the "Fridericiana", merged with the Karlsruhe Research Center (), which had originally been established in 1956 as a national nuclear research center (, or KfK). KIT is a member of the TU9, an incorporated society of the largest and most notable German institutes of technology.TU9 As part of the German Universities Excellence Initiative KIT was one of three universities which were awarded excellence status in 2006. In the following "German Excellence Strategy" KIT was awarded as one of eleven "Excellence Universities" in 2019. KIT is among the leading technical universities in Germany and Europe. According to different bibliometric ranking ...
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Ruprecht-Karls-Universität Heidelberg
} Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest university and one of the world's oldest surviving universities; it was the third university established in the Holy Roman Empire. Heidelberg is one of the most prestigious and highly ranked universities in Europe and the world. Heidelberg has been a coeducational institution since 1899. The university consists of twelve faculties and offers degree programmes at undergraduate, graduate and postdoctoral levels in some 100 disciplines. The language of instruction is usually German, while a considerable number of graduate degrees are offered in English as well as some in French. As of 2021, 57 Nobel Prize winners have been affiliated with the city o ...
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Ludwig Otto Hesse
Ludwig Otto Hesse (22 April 1811 – 4 August 1874) was a German mathematician. Hesse was born in Königsberg, Prussia, and died in Munich, Bavaria. He worked mainly on algebraic invariants, and geometry. The Hessian matrix, the Hesse normal form, the Hesse configuration, the Hessian group, Hessian pairs, Hesse's theorem, Hesse pencil, and the Hesse transfer principle are named after him. Many of Hesse's research findings were presented for the first time in ''Crelle's Journal'' or Hesse's textbooks.MacTutor History of Mathematics archive and Complete Dictionary of Scientific Biography Life Hesse was born in Königsberg (today Kaliningrad) as the son of Johann Gottlieb Hesse, a businessman and brewery owner and his wife Anna Karoline Reiter (1788–1865). He studied in his hometown at the Albertina under Carl Gustav Jacob Jacobi. Among his teachers were count Friedrich Wilhelm Bessel and Friedrich Julius Richelot. He earned his doctorate in 1840 at the University of König ...
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Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a dissertation. The degree, abbreviated "Dr. habil." (Doctor habilitatus) or "PD" (for "Privatdozent"), is a qualification for professorship in those countries. The conferral is usually accompanied by a lecture to a colloquium as well as a public inaugural lecture. History and etymology The term ''habilitation'' is derived from the Medieval Latin , meaning "to make suitable, to fit", from Classical Latin "fit, proper, skillful". The degree developed in Germany in the seventeenth century (). Initially, habilitation was synonymous with "doctoral qualification". The term became synonymous with "post-doctoral qualification" in Germany in the 19th century "when holding a doctorate seemed no longer sufficient to guarantee a proficient transfe ...
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Privatdozent
''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifications that denote an ability (''facultas docendi'') and permission to teach ('' venia legendi'') a designated subject at the highest level. To be granted the title Priv.-Doz. by a university, a recipient has to fulfill the criteria set by the university which usually require excellence in research, teaching, and further education. In its current usage, the title indicates that the holder has completed their habilitation and is therefore granted permission to teach and examine students independently without having a professorship. Conferment and roles A university faculty can confer the title to an academic who has a higher doctoral degree - usually in the form of a habilitation. The title, ''Privatdozent'', as such does not imply a sala ...
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